Comment by joha4270

The satellite moves, so every orbit it captures a globe spanning strip that is 50 miles wide (here uncritically accepting the 50 miles figure).

And the carrier isn't going to be in the middle of the pacific, its going to want to launch strikes, so its going to be within (say 500 miles) of Chinese military targets, which does narrow down the size of the haystack somewhat.

But yes, this is a significant challenge. On the modern battlefield it is usually significantly harder to find something than to kill something after you have found it.